Lock-in Amplification:
Lock-in amplification is a widely used technique to recover a signal of interest. It is a particular type of demodulation with specific requirements to the filter performance and flexibility in setting the demodulation frequency. Demodulation is performed on the measured signal in order to obtain the phase and the amplitude of the signal of interest at a specific frequency. Lock-in amplification is equally used to narrow band signal and wide band signal analysis.
FIG. 1 shows a conventional analog lock-in amplifier (LIA). An analog input signal s(t) around a center frequency f0 is multiplied with the signals sin (2πf0t) and cos (2πf0t), revealing the so-called in-phase and out-of-phase component of the signal. The fundamental frequency f0 is extracted from a reference signal r(t). By this operation, the center frequency of the input signal is shifted to DC or an intermediate frequency and unwanted frequency components are removed by the subsequent low-pass filter. The output d(t) of the lock-in amplifier represents amplitude and phase of the input signal around f0.
In a digital lock-in amplifier, all calculations are carried out with digital numbers in a virtually error-free manner. The main source for non-idealities is the performance of the analog-to-digital converter. A digital lock-in amplifier is shown in FIG. 2. The basic principle is the same as for the analog lock-in amplifier, but the input signal is converted to digital values before it is being demodulated by the multiplier and fed to the subsequent low-pass filter. The reference signal is also digitized, often by means of a simple comparator. The remaining operations are the same as for the analog lock-in amplifier, but they are conducted in the digital domain. A digital implementation has several advantages since drift problems, non-linearity and non-idealities in multiplication or filtering are basically non-existent.
Phase-Synchronous Processing:
Phase-synchronous processing (PSP) can be applied if a signal of interest is periodic and if knowledge of the fundamental frequency f0 of the signal is available. In PSP, a given number of periods of the signal of interest is combined in order to obtain a phase-domain signal. A block diagram of a PSP unit is depicted in FIG. 3. The input signal s(t) and the reference signal r(t) are periodic with the same fundamental frequency f0 (T0=1/f0). Based on the reference signal r(t), the phase signal Φ(t) (in [0, 2π)) is derived. Note that the phase signal starts at 0 and increases linearly to 2π for each successive period of the reference signal. At each time instant t, the value of the input signal s(t) is associated with the actual phase Φ(t). Thereby, for each phase value Φ we obtain a sequence <S>(Φ) of signal values. Subsequently, the individual sequences are processed according to a given PSP operation, yielding the output <s>(Φ).
A well-known instance of this type of processing is phase-synchronous averaging, also known as time-synchronous averaging: multiple period snapshots are averaged in order to reduce noise components of the input signal.
In a digital implementation of PSP, the input signal s(t) and the reference signal r(t) are first converted to digital values. The subsequent processing is then carried out in the digital domain (see FIG. 4).